0000000000011782
AUTHOR
Dietmar Leisen
Dynamic Risk Taking with Bonus Schemes
This paper studies dynamic risk taking by a risk-averse manager who receives a bonus; the company may default on its contractual obligations (debt and fixed compensation). We show that risk taking is time independent, and is summarized by the so-called risk aversion of derived utility. We highlight the importance of dynamic aspects and provide a foundation for common qualitative discussions that are based on characteristics of bonus functions. The paper cautions that deferral of fixed compensation may increase risk taking. Finally, we motivate a new bonus scheme that incentivizes the manager to implement the socially optimal risk level.
Valuation of Barrier Options in a Black-Scholes Setup with Jump Risk
This paper discusses the pitfalls in the pricing of barrier options approximations of the underlying continuous processes via discrete lattice models. These problems are studied first in a Black-Scholes model. Improvements result from a trinomial model and a further modified model where price changes occur at the jump times of a Poisson process. After the numerical difficulties have been resolved in the Black-Scholes model, unpredictable discontinuous price movements are incorporated.
The shape of small sample biases in pricing kernel estimations
AbstractNumerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that est…
Staged Venture Capital Contracting with Ratchets and Liquidation Rights
Abstract This paper uses real options analysis to study later round financing in the presence of two standard venture capital contracting provisions: anti-dilution (ratchet) and liquidation preference. We argue that such provisions can preclude financing of a positive NPV venture in the case of a large follow-on financing relative to firm value. Liquidation preference contracting at multiples greater than one is not feasible in the later round if the financing is small relative to firm value. We highlight an interaction effect between the two provisions: increasing the liquidation multiple can help to avoid dilution and the need for the prior venture capitalist to waive ratchet provisions.
Minimal Dynamic Equilibria
We define dynamic models as multiperiod models with no static representations and demonstrate that current prevalent asset pricing empirical implementations are inconsistent with dynamic equilibria. Specifically, empirical implementations are misspecified with respect to three essential asset pricing questions (TEQ): dependency on higher moments, complexity of risk premia, and mean-variance efficiency of the “market portfolio” (ability to proxy pricing kernels/SDFs). While we already know that “Merton” models, and their derivatives, differ from static models in all TEQ, we show that this is the case even the “minimal” dynamic equilibria.
Equilibrium open interest
Abstract This paper analyses what determines an individual investor's risk-sharing demand for options and, aggregating across investors, what the equilibrium demand for options. We find that agents trade options to achieve their desired skewness; specifically, we find that portfolio holdings boil down to a three-fund separation theorem that includes a so-called skewness portfolio that agents like to attain. Our analysis indicates also, however, that the common risk-sharing setup used for option demand and pricing is incompatible with a stylized fact about open interest across strikes.
Contract and Asset Values in Venture Capital Financings
In venture capital financings a venture capitalist buys some fraction of a company, for a stated amount of money, through preferred shares. It is common practice in empirical and theoretical analyses to infer from this transaction a value for the entire company, which we call the contract value. Owners do not hold shares with the same rights and so the contract value misrepresents the company value of all assets (asset value). This paper studies a stylized venture capital market, calculates the ratio of contract to asset value, and derives the expected returns both at the level of venture capital funds and at the company level. We study quantitatively the impact on econometric analyses and …
Building a Consistent Pricing Model from Observed Option Prices
This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option prices. It explicitly treats the fact that only a discrete data set can be observed in practice. The framework is general and allows for state dependent volatility and jumps. The theoretical properties are studied. An easy procedure to check for arbitrage opportunities in market data is proved and then used to ensure the feasibility of our approach. The implementation is discussed: testing on market data reveals a U-shaped form for the "local volatility" depending on the state and, surprisingly, a large probability for strong price movements.
The Random-Time Binomial Model
In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence of the values for European and American put options. Differently to the CRR-model the convergence behaviour is extremely smooth in our model. By using extrapolation we therefore achieve order of convergence two. This way it is an efficient tool for pricing purposes in the Black-Scholes setup, since the CRR model and its extrapolations typically achieve order one. Moreover our model allows in a straig…
Proportional Small Sample Bias in Pricing Kernel Estimations
Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In a first step, we analyze theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader of potential computational issues coupled with statistical techniques. In a second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kern…
Investing for the Long Run
This paper studies long term investing by an investor that maximizes either expected utility from terminal wealth or from consumption. We introduce the concepts of a generalized stochastic discount factor (SDF) and of the minimum price to attain target payouts. The paper finds that the dynamics of the SDF needs to be captured and not the entire market dynamics, which simplifies significantly practical implementations of optimal portfolio strategies. We pay particular attention to the case where the SDF is equal to the inverse of the growth-optimal portfolio in the given market. Then, optimal wealth evolution is closely linked to the growth optimal portfolio. In particular, our concepts allo…
Systemic Risk in a Structural Model of Bank Default Linkages
Abstract We study a structural model of individual bank defaults across the banking sector; banks are interconnected through their exposure to a common risk factor. The paper introduces a systemic risk measure based on the default frequency in the banking sector; this measure depends non-linearly on the factor's loadings, in contrast to previous systemic risk measures that depend linearly on loadings. We estimate loadings in the U.S. banking system over the course of the last 36 years; we find that they have considerably increased over time and identify four major regimes. Our measure shows that systemic risk became critical in the last of our four regimes, covering the most recent time per…
Does bonus deferral reduce risk-taking?
AbstractThe common thinking that deferring bonus payments makes an agent more risk averse isfalse. We characterize continuous-time risk taking and show that the introduction of deferralincreases risk taking at any time when the realized asset value is large or small. For realizedasset values in-between we characterize the parameterizations of deferral for which risk tak-ing decreases and discuss trade-offs in setting the deferral parameters.Keywordsbonus, risk taking, risk aversion, deferral ratioJEL Classi cationG28, G38 ∗ This paper circulated previously under the title \Bonus Deferral Does Not Choke Excessive Risk Taking."We are grateful for comments and suggestions from seminar participa…
Were Prestigious Independent Directors Responsible for the Subprime Crisis?
We study the independence ratio, as well as the prestige, reputational incentives, experience, and financial expertise of independent directors for 767 U.S. banks from 2000 to 2015, to concentrate on causes of the subprime crisis: short-termism, poor monitoring, and excessive risk-taking. We find that higher independence ratios decrease the monitoring quality of the board, increase short-term incentives for the CEO, and promote greater subprime risk-taking. Our results thereby suggest that, while official responses to the subprime crisis claim that banks were not independent enough, rising independence ratios following Enron and Sabanes Oxley were a major contributing cause of the subprime …
Valuing Common and Preferred Shares in Venture Capital Financing
Abstract This article compares five different methodologies to value common and preferred shares with liquidation rights in a single-period setup of venture capital financing: the venture capital (VC) method; discounted cash-flow valuation with the Capital Asset Pricing Model (CAPM); discounted cash-flow valuation with market model in logs; a risk-preference-based approach; and the real options approach. The risk preference and the real option methodologies are the only ones that can properly account for the contingency in preferred stock. With small financings and small multiples the choice of methodology is not critical; however, with stronger preference rights, the VC method, the CAPM, a…
A Perturbation Approach to Continuous-Time Portfolio Selection Under Stochastic Investment Opportunities
This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.
A Partial Equilibrium Model of Option Markets
This paper addresses the questions who is buying and who is selling options on a stock, the optimal position to hold, and how this affects the price. The individual demand functions and the equilibrium allocation are derived using an asymptotically valid expansion. Trading occurs only at discrete dates; the option does not have to complete the market. The paper also discusses the conditions under which trade results, the importance of heterogeneity for trade, when preferences become irrelevant to price options, and the case in which there is only a spanning demand, but no risk-sharing demand in options.
Aggregation of preferences for skewed asset returns
This paper characterizes the equilibrium demand and risk premiums in the presence of skewness risk. We extend the classical mean-variance two-fund separation theorem to a three-fund separation theorem. The additional fund is the skewness portfolio, i.e. a portfolio that gives the optimal hedge of the squared market return; it contributes to the skewness risk premium through co-variation with the squared market return and supports a stochastic discount factor that is quadratic in the market return. When the skewness portfolio does not replicate the squared market return, a tracking error appears; this tracking error contributes to risk premiums through kurtosis and pentosis risk if and only …
How Bonus Deferral Changes Risk Taking
We characterize continuous-time risk taking and show that the introduction of deferral increases risk taking at any time when the realized asset value is large or small. For realized asset values in-between we derive the parameterizations of deferral for which risk taking decreases and discuss trade-offs in setting the deferral parameters.
A Top-Down Method for Long-Term Investing
This paper bases long-term investing on a tradeable stochastic discount factor (SDF), relates it to the growth optimal portfolio and argues for a top-down method, where modeling efforts are directed at capturing its long-run dynamics in a generalized setting. This differs from the common, cumbersome bottom-up method of modeling many risky securities in the marketplace. Various optimal portfolio strategies can be implemented efficiently using fractional expectations of the SDF. This paper illustrates empirically for the US stock market that the proposed method leads to higher wealth, higher returns on investment and higher long-term utility levels.
HETEROGENEITY IN RISK PREFERENCES LEADS TO STOCHASTIC VOLATILITY
This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are he…